# The Mathematical Art of M.C. Escher

## For me it remains an open question whether [this work]

pertains to the realm of mathematics or to that of art.

## —M.C. Escher

### Introduction

Maurits Cornelis Escher created unique and fascinating works of art that explore and exhibit a wide range of mathematical ideas.

He was born in Leeuwarden, Holland in 1898, and when he was in school his family planned for him to follow his father’s career of architecture. However, poor grades and an aptitude for drawing and design eventually led him to a career in the graphic arts, specializing in woodcuts, mezzotints, and lithographs.

His work went almost unnoticed until the 1950’s, but by 1956 he had given his first important exhibition, was written up in *Time* magazine, and acquired a world-wide reputation. Among his greatest admirers were mathematicians, who recognized in his work an extraordinary visualization of mathematical principles. This was the more remarkable in that Escher had no formal mathematics training beyond secondary school.

His work eventually appeared not only in printed form, but as commissioned or imitative sculptures on public buildings, as decorations on everything from neckties to mousepads, and in software written to automate the reproduction and manipulation of tesselations. Reproductions of his work remain in strong demand, and he has inspired thousands of other artists to pursue mathematical themes in their own work. He is of course also much imitated.

As his work developed he drew great inspiration from the mathematical ideas he read about, often working directly from structures in plane and projective geometry, and eventually capturing the essence of non-Euclidean geometries, as we will see below. He was also fascinated with paradox and “impossible” figures, and used an idea of Roger Penrose’s to develop many intriguing works of art. Thus, for the student of mathematics, Escher’s work encompasses two broad areas: the geometry of space, and what we may call the *logic* of space.

Contributors

- B. Sidney Smith, author

Citation Info

- [MLA] Smith, B. Sidney. "The Mathematical Art of M.C. Escher."
*Platonic Realms Minitexts.*Platonic Realms, 13 Mar 2014. Web. 13 Mar 2014. <http://platonicrealms.com/> - [APA] Smith, B. Sidney (13 Mar 2014). The Mathematical Art of M.C. Escher. Retrieved 13 Mar 2014 from
*Platonic Realms Minitexts:*http://platonicrealms.com/minitexts/Mathematical-Art-Of-M-C-Escher/